Question

Consider four points in a plane such that there exists an unit disk covering any three of them. Prove that there exists an unit disk covering all those four points

Answer 1

so we need unit that satisfies

Answer 2

yes we need to prove there exists some unit disk covering all four points

Answer 3

ok i can only think of one method, minimizing the area of the three small unit disks

Answer 4

hmm but sounds like giving a condition

Answer 5

im reading this..
http://en.wikipedia.org/wiki/Helly's_theorem

Answer 6

oh i thought of discrete disk problem only

Answer 7

whats that ?

Answer 8

http://arxiv.org/abs/1209.2951